Post on 16-Jan-2016
GLE 0701.5.5 Explore the concept of premises, including false
premises.
Intro to Logic
ValidityWhat is logic?
ValidityWhat is logic?
A science that evaluates arguments.
Validity - True or False? All cats are mammals All mammals are
animals All cats are animals.
All cats are mammals All mammals are feline All cats are feline.
All cats are mammals Circles are round All cats are animals.
All cats are mammals All mammals are
animals Circles are squares.
ValidityT All cats are mammalsT All mammals are
animalsT All cats are animals.
T All cats are mammalsF All mammals are felineT All cats are feline.
T All cats are mammalsT Circles are roundT All cats are animals.
T All cats are mammalsT All mammals are
animalsF Circles are squares.
ValidityT All cats are mammalsT All mammals are
animalsT All cats are animals.
Good Argument
T All cats are mammalsF All mammals are felineT All cats are feline.
Bad Argument
T All cats are mammalsT Circles are roundT All cats are animals.
Bad Argument
T All cats are mammalsT All mammals are
animalsF Circles are squares.
Bad Argument
ValiditySay it with me:
Truth is not enough to make an argument good!
Truth is not enough to make an argument good!
Truth is not enough to make an argument good!
Validity
Truth Validity
Good Argument
ValidityT All cats are mammalsT All mammals are
animalsT All cats are animals.
Good Argument
T All cats are mammalsF All mammals are felineT All cats are feline.
Bad Argument
T All cats are mammalsT Circles are roundT All cats are animals.
Bad Argument
T All cats are mammalsT All mammals are
animalsF Circles are squares.
Bad Argument
Validity - Can you fill in the blanks? All A are B . All B are C . All A are C .
Good Argument
All A are B . All B are C . All A are C .
Bad Argument
All A are B . C are D . All A are E .
Bad Argument
All A are B . All B are C . D are E .
Bad Argument
Validity All A are B . All B are C . All A are C .
All A are B . All B are C . All A are C .
All A are B . C are D . All A are E .
All A are B . All B are C . D are E .
Validity All A are B . All B are C . All A are C .
All A are B . All B are C . All A are C .
T All cats are mammalsT All mammals are
animalsT All cats are animals.
Good Argument
T All cats are mammalsF All mammals are felineT All cats are feline.
Bad Argument
Validity All A are B . All B are C . All A are C .
Valid
All A are B . All B are C . All A are C .
Valid
T All cats are mammalsT All mammals are
animalsT All cats are animals.
Good Argument
T All cats are mammalsF All mammals are felineT All cats are feline.
Bad Argument
ValidityT All cats are mammalsT Circles are roundT All cats are animals.
Bad Argument
T All cats are mammalsT All mammals are
animalsF Circles are squares.
Bad Argument
All A are B . C are D . All A are E .
Invalid
All A are B . All B are C . D are E .
Invalid
Validity
Truth Validity
Good Argument
Validity
Truth Validity
Sound Argument
Validity
Truth + Validity = Soundness (i.e. a good
argument)
Validity
Is a valid argument a true argument?
Validity
Is a valid argument a true argument?
No! A valid argument is one with a form that ensures if the premises
are true, then the conclusion will be
true.An argument where the conclusion
follows from the premises.
Validity
An argument is valid if when the premises
are true, the conclusion has to be true.
Validity
An argument is sound if it is valid, and the
premises are true.
VALID INVALID
True Premises +
True Conclusion
True Premises +
False Conclusion
False Premises +
True Conclusion
False Premises +
False Conclusion
VALID INVALID
True Premises +
True Conclusion True Premises +
False Conclusion False Premises +
True Conclusion False Premises +
False Conclusion
ValidityValidity InvalidityVALID INVALID
True Premises +
True Conclusion
True Premises +
False Conclusion
False Premises +
True Conclusion
False Premises +
False Conclusion
ValidityValidityTo show that it
is impossible
for an argument
to have true
premises and
a false conclusion we have to
InvalidityTo show that it
is possible for
an argument
to have true
premises and
a false conclusion we simply have
to come up with an example where this occurs.
VALID INVALID
True Premises +
True Conclusion
True Premises +
False Conclusion
False Premises +
True Conclusion
False Premises +
False Conclusion
construct a proof via the rules of logic. This is why the rules are how they are.
Proof Counter-example
Pop-quiz!Is a valid argument contain
all truths?Is an argument that contains
all truths a good argument?Can premises be valid?Can a valid argument have a
false conclusion?Can an argument be true?How do you show invalidity?